Splitting Lemma
SplitSysUnivariate splits (whenever possible) the input matrix in the specified variable up to the order chosen (6 in the following example). It returns the dimension of the first square block, the transformation matrix, and the equivalent block-digonalised system.
| > | ![A := `/`(`*`(Matrix(2, 2, [`+`(`*`(2, `*`(`^`(t, 3))), 2), `+`(`-`(`*`(2, `*`(`^`(t, 2)))), `-`(2)), -2, `+`(`-`(`*`(`^`(t, 3))), `-`(`*`(4, `*`(t))), 2)])), `*`(`^`(t, 4))); 1; r, T, B := SplitSysUni...](images/miniISOLDE_examples_16.gif){kind=small} |
 |
|
  |
(1.1) |
| > |  |
 |
|
 |
(1.2) |
SplitLemmaUnivariate decouples the equivalent system in the output:
| > |  |
 |
(1.3) |
| > |   |
 |
|
   |
(1.4) |
| > |   |
 |
|
 |
(1.5) |
The following system is not decoupled via the Splitting Lemma:
| > |   |
 |
|
 |
(1.6) |
| > |
| > |   |
 |
|
          |
|
         |
(1.7) |
| > |